# ZX BASIC:FSin.bas

## Introduction

**fSin** is the basis for the alternatives, since COS(x) can be calculated from SIN(x) and TAN(x) from COS(x) And SIN(x).

The functions should be accurate to about 0.25%, and significantly faster. If you need a lot of trig in your code, and it doesn't need to be pinpoint accuracy, these are good alternatives. Note that they more or less acknowledge they are less accurate by returning values of type FIXED instead of type FLOAT. I did this because it should be fine for the actual accuracy returned, and FIXED numbers process faster and smaller than FLOAT ones.

- Note that you need only include fSin if you only want Sines, but you need fSin to use fCos or fTan.

- Note that these functions use degrees, not radians.

### SINE Function

FUNCTION fSin(num AS FIXED) AS FIXED DIM quad AS BYTE DIM est1,dif AS UBYTE num = num MOD 360 'This change made now that MOD works with FIXED types. 'This is much faster than the repeated subtraction method for large angles (much > 360) 'while having some tiny rounding errors that should not significantly affect our results. 'Note that the result may be positive or negative still, and for SIN(360) might come out 'fractionally above 360 (which would cause issued) so the below code still is required. WHILE num>=360 num=num-360 END WHILE WHILE num<0 num=num+360 END WHILE IF num>180 THEN quad=-1 num=num-180 ELSE quad=1 END IF IF num>90 THEN num=180-num: END IF num=num/2 dif=num : REM Cast to byte loses decimal num=num-dif : REM so this is just the decimal bit est1=PEEK (@sinetable+dif) dif=PEEK (@sinetable+dif+1)-est1 : REM this is just the difference to the next up number. num=est1+(num*dif): REM base +interpolate to the next value. RETURN (num/255)*quad sinetable: ASM DEFB 000,009,018,027,035,044,053,062 DEFB 070,079,087,096,104,112,120,127 DEFB 135,143,150,157,164,171,177,183 DEFB 190,195,201,206,211,216,221,225 DEFB 229,233,236,240,243,245,247,249 DEFB 251,253,254,254,255,255 END ASM END FUNCTION

### COSINE Function

FUNCTION fCos(num AS FIXED) AS FIXED RETURN fSin(90-num) END FUNCTION

### TANGENT Function

FUNCTION fTan(num AS FIXED) AS FIXED RETURN fSin(num)/fSin(90-num) END FUNCTION